The structure of hyperfinite stochastic integrals by Tom L. Lindstr0m, University of Oslo. 1. Introduction. The hyperfinite theory for stochastic integration goes back to R.M. Anderson [2], who constructed a Brownian motion as the standard part of a hyperfinite random walk, and defined the sto- chastic integral with respect to this random walk as a pathwise Stieltjes integral. The theory was further developed by H.J. [7], and extended to more general classes of martingales by [9], and Hoover ruld Perkins (6], independently (confer also the work of K.Do Stroyan)$ A further extension to the infinite dimen- sional case was given in [10]. The papers by Keisler and Hoover- Perkins effectfully demonstrated the power of the nonstandard approach by proving new strong existence results for stochastic differential equations. A central issue in the first papers was to show that what could be obtained by the standard theory could also be obtained by the hyperfinite theory, it was shown in [9] that if 0 + M is the "right standard part" of a hyperfinite SL 2 -martingale,and X 0. + is a process standard integrable with respect to".. M , then there exists a hyperfinite process y- called a 2-lifting of X-- which is integrable \IJi th respect to M, and such that 0 cJYdM)+ = rxd 0 M+. Moreover, it was shown that all local L 2 -martingales J could in a natural way be represented as right standard parts of